Mirror Symmetry for Maximally Degenerate Positive Calabi–Yau Pairs

Definitions and mathematical statement

The supplied record refers to pairs $(M,D)$ covered by a general construction of maximally degenerate positive Calabi--Yau pairs. It does not supply that construction or definitions of its hypotheses. Write $\mathcal G$ provisionally for the class of pairs covered by that construction; this notation records the intended scope but does not give an independently usable definition of the class.

Source problem. Formulate a single precise mirror-symmetry conjecture applicable to every pair $(M,D)\in\mathcal G$, and prove that conjecture in this full generality.

Unresolved qualifications. The record does not specify the ambient category or base field, the dimension or regularity of $M$, the nature of $D$, or the meanings of Calabi--Yau, positive, and maximally degenerate in the referenced construction. It also does not specify the mirror object, the structures to be compared, or the asserted correspondence. Consequently, the supplied evidence determines a research objective with universal scope, but does not determine a complete mathematical conjecture. The original statement restricts the scope to pairs covered by the referenced general construction; the shorter statement omits that restriction, and their equivalence cannot be established from the record.

Short English statement

Seek one precise mirror-symmetry conjecture and a proof covering every maximally degenerate positive Calabi--Yau pair admitted by the source's general construction. The construction, its hypotheses, and the intended mirror correspondence are missing, so a complete mathematical statement requires source clarification.

Sources

• Local UnsolvedMath registry: permanent ID $30004426$, source problem code catalogue entry, in the supplied source record for the Oberwolfach Reports Open Problems collection. Project registry locations are data/unsolvedmath/problems.json and the supplementary catalog/problems.json; neither was independently inspected for this draft. No individual proposer is supplied; the proposed year is recorded as 2020.
• Supplied report citation: Mini-Workshop: Superpotentials in Algebra and Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/10, pp. 569--600. Supplied source URL and literature-source link, labelled "original OWR report": https://doi.org/10.4171/owr/2020/10. The report contents were not independently consulted.
• Supplied dated literature curation, checked 2026-08-22: the record labels the problem open and reports that a mirror-symmetry conjecture covering all stated maximally degenerate Calabi--Yau pairs is explicitly described as open, with no general proof found. This is supplied dated curation, not an independently verified literature assessment. The background explicitly requests independent verification of time-sensitive status and cited claims.